Find the angle θ , in radians, in the given right triangle. The length of the side adjacent to θ is 16 and the length of the side opposite θ is 10. A right triangle with height 10 opposite from angle theta and base 16 adjacent to angle theta. 10 16 Round your answer to the nearest hundredth

The values are 5, 6, 8, 9 for the given function y=∛x+7.

So, option D is correct.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y.

The earliest known concept of a function was created by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. [4] At first, functions were envisioned as the perfect representation of the relationship between two variables. In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.

Given,

y=∛x+7

Let x=-8,

y=∛8+7

y=-2+7

y=5

x=-1, y=∛(-1)+7

y=-1+7

y=6

x=1, y=∛1+7

y=1+7

y=8

x=8, y=∛8+7

y=2+7

y=9

Therefore, the values are 5, 6, 8, 9

So, option D is correct

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The complete question is:

"Complete the table for the function y = ∛x+7

OA) -5, -6, -8, -9

OB) -9, -8, -6, -5

Oc9,8. 6. 5

OD) 5,6, 8, 9".

The dimensions of the rectangle are:

Length = 10 m

Width = 6.5 m

Recall that the area of aa rectangle is given as, length × width.

Given the following:

Area of the rectangle = 65 m²

Let the width of the rectangle be represented as w.

Length of the rectangle = 2w - 3 m

Therefore:

(2w - 3)(w) = 65

Expand:]

2w² - 3w = 65

2w² - 3w - 65 = 0

Factorize:

w = 6.5 or w = -5

The width cannot be negative, therefore, the width = 6.5 m.

Length of the rectangle = 2w - 3 = 2(6.5) - 3 = 10 m

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Answer: 8/-9

Step-by-step explanation:

If h(7), plug in 7 into all the x-values.

=[tex]\frac{7^{2}-5(7)-6}{7^{2}-6(7)-16 }[/tex]

=[tex]\frac{49-35-6}{49-42-16}[/tex]

=[tex]\frac{8}{-9}[/tex]

At 9 AM Bob could declare the pool was full of water, using given information about fill rate, discharge rate and time.

What is fill rate and discharge rate ?

The definition of fill rate is the percentage of customers orders you are able to meet without running out of stock at any given time.

The discharge rate is the amount of fluid that is passing through a given cross sectional area per unit time.

We need to divide it in 3 parts:

Part 1: When only 1 hose is filling the pool at 3 gal per hr.

Part 2 : When after 10 hours animals started drinking water .

Part 3: When 2nd hose also started at the rate 2 gal per hr.

Part 1:

For 10 hours it get started . So, pool get filled is 30gal.

Part 2:

After 10 hours, rate decreased by animals at 1 gal/hour.

So, rate = 3-1 = 2 gal/hour.

So, water filled for 5 hour = 10 gal.

So, total pool is filled = 10 + 30 = 40 gal.

Remaining = 60 - 40 = 20 gal.

Part 3:

2nd hose is added at the rate 2gal/hour.

Now, rate = 2+2 = 4 gal/hour.

Time taken for 20 gal = 5 hours.

So, total time taken = 10 + 5 +5

                                 = 20 hours.

We need to find the time ,

Time at which water is started = 1pm

1PM + 11hours = 12AM

For remaining , 9 hours

12AM + 9hours = 9AM.

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Congruent triangles are triangles having corresponding sides and angles to be equal.

Congruent triangles are triangles that have both the same size and the same shape and they have the same perimeter and the same area. Congruence is denoted by “≅”.  For example, we can write ABC ≅ DEF. They have the same area and the same perimeter.

Congruent triangles have the same angle measures and the same side lengths.

On the other hand, the similar triangle is the term used for triangles that have the same shape, but not necessarily the same size.

Two triangles are considered to be congruent if they meet one of the following criteria.

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The volume of the gas at 6.4 × 10⁴ Pascals is 7.44×10⁻⁷m³.  The pressure of the gas is  5.47× 10⁶ Pascals

At a constant temperature, the volume of a gas is inversely proportional to its pressure. We can write:

V α 1/P

V = T/P   (where T is the constant of proportionality)

T = PV

SInce T₁ = T₂

Also, P₁V₁ = P₂V₂

We have pressure of 2.8 x 10⁶ Pascals and a volume of 1.7 x 10⁻⁸ m³

a) What will the volume of the gas be when its pressure is 6.4 × 10⁴ Pascals?

P₁V₁ = P₂V₂

2.8 × 10⁶ × 1.7×10⁻⁸ = 6.4 × 10⁴ × V₂

V₂ = (2.8 × 10⁶ × 1.7×10⁻⁸)/ (6.4 × 10⁴)

V₂ = 7.44×10⁻⁷m³

b) Work out the pressure of the gas when its volume is 8.7 x 10⁻⁹ m³

P₁V₁ = P₂V₂

2.8 × 10⁶ × 1.7×10⁻⁸  = 8.7 ×10⁻⁹ × P₂

P₂ = (2.8 × 10⁶ × 1.7×10⁻⁸)/ (8.7 ×10⁻⁹)

P₂ =  5.47× 10⁶ Pascals

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Answer:

I think its (-4,2)

Step-by-step explanation:

Answer:

It's 37

Step-by-step explanation:

Answer: 37

Step-by-step explanation:

[tex]\displaystyle\\20-(2)(-7)+(-9)\div(-3)=\\\\20-(-14)+\frac{-9}{-3}=\\\\20+14+3=\\\\37[/tex]

Answer:

Step-by-step explanation:

1. Multiply 9 times 4t in parentheses

2. Once you get the answer you add it to 3t and that gives you 39t

Is this question any helpful enough for?

The z-score for Johnny’s grade is 1.92.

Johny's score falls into the 97.28 percentile

What is a normal distribution?

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical representation of data around its mean value. It is represented graphically as the "bell curve."

Here, we have

mean = 69.5, std. deviation = 6.5 , x = 82

A. By normal distribution formula,

  z = ( x - mean) / std. deviation

  z = (82 - 69.5) / 6.5

 = 1.92

Hence, the z-score for Johnny’s grade is 1.92.

B. P(z<1.92) = 0.9728

Hence, Johny's score fall into 97.28 percentile.

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Sleep hours per night is independent.

Given the data:

Hours of Sleep 39 or younger 40 or older

> 6 _____38 36

6 to 6.9 _ 61 58

7 to 7.9 __76 74

8 or more 65 92

The analysis will be conducted using the Chisquare statistic:

The supposition

H0: The amount of sleep each night is independent

H1: The amount of sleep each night is not independent

χ² = (observed - Expected) (observed - Expected)2 / Predicted

to speed up computation. To conduct the analysis, we might utilize a Chisquare calculator:

The evaluation statistic is 4.0061.

Row - 1 * The degree of freedom (column - 1)

Degree of freedom is equal to (4-1)*(2-1)=3*1=3.

Pvalue is 0.261.

Since Pvalue >, we are unable to reject the hypothesis that sleep duration is independent total %

> 6 _____38 36_ 74 _ 14.8

6 to 6.9 61 58 _ 119 23.8

7 to 7.9 __76 74 150 30

8 or higher 65 92 157 31.4

_______240 260 500 100

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There are 3 more days will it take her to plant all the trees.

What is rate?

The numerator of a ratio in mathematics represents the rate of change in the other (dependent) variable if the denominator of the ratio is expressed as a single unit of one of the related quantities and it is assumed that this quantity can be changed systematically (i.e., is an independent variable).

Given:

Tamika must plant 432 trees.

In the past 6 days Tamika planted 288 trees.

She continues the planting tree at the same rate.

As she planted 288 trees in 6 days.

That means she plant 288 / 6 = 48 trees in a day.

The remaining trees are 432 - 288 = 144.

So, 144 trees will be planted in 144 / 48 = 3 days.

Hence, there are 3 more days will it take her to plant all the trees.

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Therefore option a) 5x+4 is the simplified form of the equation.

Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.

Here,

Given:

=>(−3x − 12) + (16 + 8x)

=> -3x-12+16+8x

=> 5x+4

So 5x+4 is the simplified form of the equation

Therefore option a) 5x+4 is the simplified form of the equation

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The time required for the total amount in Harrison's account to reach $410 is 4.49 years.

The simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

A/P - 1 =  rt

t = ( A/P - 1 ) / r

t = ( $410/$345 - 1 ) / 0.042

t = ( 13/69 ) / 0.042

t = 4.49 years

Therefore, the time needed to reach accrued amount is 4.49 years.

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(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph thus option (B) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.

As per the given coordinates,

The coordinate is the representation of horizontal and vertical distinctions.

The (3,1) is the point that is 3 grid right or horizontal and 1 unit up or vertical from the origin.

Hence "(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph".

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The given trigonometric equations have the value tan x, -cot x.

Since the given trigonometric equations  are: cos2x-cos4x/sin2x+sin4x   and  cos2x+cos4x/sin2x-sin4x. The problem is related to trigonometric Ratios, which are the ratios of the side of a right-angled triangle.Now for the equation (cos 2x - cos 4x )/(sin2x +sin4x)

since we know the formulas  :

cos A + cos B = - sin (A+B)/2 sin(A-B)/2

sin A - sin B = sin( A+B)/2 cos (A-B)/2

so for the equation, we can

= (-sin 3x) sin ( -2x)/2)/( cos 3x cos x)

= sin 3x sin x/ (sin 3x) cos x

= tan x

for the second equation    cos2x+cos4x/sin2x-sin4x

= cos 3x cosx/ cos3x sin(- x)

= - cot x

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Therefore the solution to the given problem is  the each of the congruent base angles is 70°

In Euclidean geometry, an angle is the figure generated by two rays, called the sides of the angle, sharing a common termination, called the vertex of the angle. Angles created by two rays are in the plane where the rays are located. The intersection of two planes also forms angles. We refer to these as dihedral angles.

Here,

As the triangle is an isosceles triangle therefore it will have 2 same angles

thus,

Sum of the 3 angles of a triangle=180°

Vertex angle =40°

Sum of two congruent angles=180°–40°=140°

Measure of each base angle=70°

Therefore the each of the congruent base angles is 70°

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Answer:

1.14x = 19.38

$17

Step-by-step explanation:

Let the price before delivery charge = x.

The charge is 14%, so it is 14% of x, or 0.14x.

The original price plus charge is x + 0.14x, or 1.14x.

1.14x = 19.38

x = 19.38/1.14

x = 17

The price is $17

Answer:

The answer is 2.9

Step-by-step explanations are not quite accurate

After solving, the surface integral S is [tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14.

In the given question, we have to evaluate the surface integral.

(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.

Now the surface integral is:

[tex]\int\int_{S}(x + y + z) dS[/tex]

x = u+v, y = u−v, z = 1+2u+v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6

The parametric curve is

r(u,v) = <u+v, u−v, 1+2u+v>

Then surface integral is calculated as

[tex]\int\int_{S}(x + y + z) dS=\int\int_{A}f(x(u,v), y(u,v), z(u,v))|r_{u}\times r_{v}| dudv[/tex]

Now find partial derivatives of parametric curve with respect to u and v

[tex]r_{u}[/tex](u,v) = <1, 1, 2>

[tex]r_{v}[/tex](u,v) = <1, -1, 1>

Now find cross product

[tex]r_{u}\times r_{u}[/tex] = <1, 1, 2> × <1, -1, 1>

[tex]r_{u}\times r_{u}[/tex] = <1+2, 2-1, -1-1>

[tex]r_{u}\times r_{u}[/tex] = <3, 1, -2>

Now parametric function is

x+y+z = u+v+u-v+1+2u+v

x+y+z = 4u+v+1

Then the surface integral is:

[tex]\int\int_{S}(x + y + z) dS=\int^{6}_{0}\int^{8}_{0}(4u+v+1)\sqrt{14}dudv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(4\frac{u^2}{2}+uv+u)^{8}_{0}dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}[(4\frac{(8)^2}{2}+8v+8)-(4\frac{(0)^2}{2}+0\cdotv+0)]dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(128+8v+8)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(136+8v)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}(136v+8\frac{v^2}{2})^{6}_{0}[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}[(136\times6+8\frac{6^2}{2})-(136\times0+8\frac{0^2}{2})][/tex]

[tex]\int\int_{S}(x + y + z) dS[/tex] = √14×(816+144)

[tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14

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For given data of ten professional athletes:

A) A scatter plot of the data is as shown below.

B) An equation of the line of best fit is:

y = 1.7946x + 2.1956

C) The line of best fit on the scatter plot is as shown below.

D) The y-intercept of the line of best fit is: a = 2.1956

The y-intercept represents, on average players with no endorsements earn million dollars each year.

In this question we have been given a random sample of ten professional athletes. In data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

A) A scatter plot of the data is as shown below.

B) For given scatter plot we can obsere that the variables show a linear regression.

And the equation of the line of best fit is:

y = 1.7946x + 2.1956

And the coefficient of regression is: R² = 0.9657

C) The line of best fit on the scatter plot is as shown below.

D) The y-intercept of the line of best fit is:

a = 2.1956

The y-intercept means that on average, players with no endorsements earn million dollars each year.

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The complete question is:

A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

x  y  x  y

0  2  5  11

3  8  4  9

2  6  3  8

1  3  0  3

6  14  5  10

A) Draw a scatter plot of the data.

B) Use regression to find the equation for the line of best fit. (Round your answers to three decimal places.)

ŷ = ____ + ____ x

C) Draw the line of best fit on the scatter plot.

D) What is the y-intercept, a, of the line of best fit? (Round your answer to three decimal places.)

a =

What does it represent? (Round your answer to three decimal places.)

The length of pregnancy does play a role in the education level of the baby. A significant relationship can be established using the chi square test.

A chi square ( χ2) test is performed in order to find a co relation between two unrelated variables. The main objective of the test is to prove whether the relationship holds true or is just a product of mere chance. For example, if we are conducting a survey of two different parameters, first being the population of people who are married and the other about their educational qualification, we will get two distinct table of values without any significant co relation. But now if we want to establish a relationship, lets say that married people have less educational qualifications, we need to prove our statement by performing a chi square test. The final value can either be a null hypothesis which states that their is no convincing relationship between the two parameters or can be a alternate hypothesis with significant co relation.

Following data can be represented on tabular form and calculated:

                                                  Gestation Period (Observed)

                                     22-27       28-32       33-36       37-42       43+    Tot

Less than high   YES    14              34            140           1010         81     1279

school degree     NO    26             65            343          3032      208   3674

                                      40             99            483          4042      289   4953

                                                   Gestation Period (Expected)

                              YES   10.32     25.56        124.72    1043.75    74.62

                              NO     29.67    73.43        358.27    2998.24   214.37

χ2 = ∑ [tex]\frac{(Observed-Expected)^2}{Expected}[/tex]

= [tex]\frac{13.54}{10.32} +\frac{71.23}{25.56} +\frac{233.47}{124.72} +\frac{1139.06}{1043.75} +\frac{40.70}{74.62} +\frac{13.46}{29.67} +\frac{233.17}{358.27} +\frac{1139.73}{2998.24}+\frac{40.57}{214.37}[/tex]

= 1.31+2.78+1.87+1.09+0.54+0.45+0.96+0.65+0.38+0.18 = 10.21

Now, calculating the degree of freedom= (coulmn-1)(row-1)= (5-1)(2-1) = 4

Looking at the reference table at 0.05 significance level, the value is 9.488

As the calculated value is more than the table value/critical value, null hypothesis can be rejected proving the alternate hypothesis that there might be a relationship between gestation period of a mother and the education level of her kid.

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a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.

b. ∅ = (Rx/Ry)

Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.

I have every vector in 2D that has both vertical and horizontal components.

There are vectors say:  A = xi + yj

                              and, B =zi + wj

For example, adding two vectors gives the result

R = (x +z)i + (y + w) j.

The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B

The direction of the angle is found as

tan∅ = Rx/Ry

     ∅ = (Rx/Ry)

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The probability to choose a group of four tiles with each tile worth one point is 0.200.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let there are total 25 tiles.

From this 20 tiles having one point each and 5 tiles having more than one point.

We have to choose a group of four tiles with each tile worth one point.

So,

probability = 4/20 = 0.200

Hence, the probability to choose a group of four tiles with each tile worth one point is 0.200.

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The population of the country in 2003 is, 368.3 million.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The exponential model a = 368.3e^0.002t describes the population,

'a' is the population of a country in millions,

t years after 2003.

We have to find the population of country in 2003.

At 2003, t = 0.

So plug t = 0 in above exponential model.

a = 368.3e^0.002(0)

a = 368.3e^0

a = 368.3

Hence, the population of the country in 2003 is, 368.3 million.

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Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To determine the probability of each of the five smallest y values, we can use the probability of each possible outcome and the number of ways that outcome can occur.

P(y = 1) = probability that the first component is defect-free = 0.8

P(y = 2) = probability that the first component is defective and the second component is defect-free = (1 - 0.8) * 0.8 = 0.16

P(y = 3) = probability that the first two components are defective and the third component is defect-free = (1 - 0.8) * (1 - 0.8) * 0.8 = 0.032

P(y = 4) = probability that the first three components are defective and the fourth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.0064

P(y = 5) = probability that the first four components are defective and the fifth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.00128

We can see that the probability of each y value is simply the probability of the previous y value multiplied by (1 - 0.8) = 0.2. This means that the probability distribution of y is given by the formula P(y) = 0.2^(y - 1) * 0.8.

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The degrees of freedom (df): For a chi-square test of independence, the df is (number of variable 1 groups − 1) * (number of variable 2 groups − 1).

Under the null speculation and sure conditions (mentioned below), the check statistic follows a Chi-Square distribution with stages of freedom identical to ( r − 1 ) ( c − 1 ) , wherein is the quantity of rows and is the quantity of columns.

The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated. The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated minus one.

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Complete question:

what degrees of freedom should be used to conduct a chi-squared test of independence using this table?

Answer:

1/3

Step-by-step explanation:

15/5=3

21/7=3

Answer: 3:1

Step-by-step explanation:

We can model this problem using ratios, we start with a ratio of 15:21 and we know we went down to a 5:7. To make both equivalent we divide both 15 and 21 by 3, meaning the ratio between the two is 3:1.

The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

As per the given graph of a function,

The time period is the time interval after curves repeat their behavior.

The given graph repeats after 1 + 1 + 1 + 1 = 4 thus period will be 4.

Hence "The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4".

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The correct options are;

a. The variables x and y also have a correlation close to 1 .

b. A scatterplot of the variables log x and y shows a strong nonlinear pattern .

The correlation is a measurement of a dependence between 2 variables. If the logarithm of the correlation function shows a linear tendency, it because the correlation between x and y shows a exponential tendency.

This mean that x and y are non linear correlated, but them are correlated.

For this type of data is used a non linear correlation technique know it as logarithm correlation.

Option c is incorrect because random patterns have a correlation value close to 0, which is not the case.

So ,

The correct options are;

a. The variables x and y also have a correlation close to 1

b. A scatterplot of the variables log x andy shows a strong nonlinear pattern

Learn more about logarithmic correlation here ;

https://brainly.com/question/29182088

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